IB Questionbank Maths SL 1
1. Find the angle between the following vectors a and b, giving your answer to the nearest degree.
a = –4i – 2j b = i – 7j
(Total 4 marks)
2. Find the size of the angle between the two vectors
2
1 and
– 8
6 . Give your answer to the nearest degree.
(Total 4 marks)
3. The vectors
– 3 2 x
x and
5 1
x are perpendicular for two values of x.
(a) Write down the quadratic equation which the two values of x must satisfy.
(b) Find the two values of x.
(Total 4 marks)
4. ABCD is a rectangle and O is the midpoint of [AB].
A B
C D
O
Express each of the following vectors in terms of OC and OD (a) CD
(b) OA (c)
AD(Total 4 marks)
IB Questionbank Maths SL 2
5. The quadrilateral OABC has vertices with coordinates O(0, 0), A(5, 1), B(10, 5) and C(2, 7).
(a) Find the vectors OB and AC .
(b) Find the angle between the diagonals of the quadrilateral OABC.
(Total 4 marks)
6. The following diagram shows quadrilateral ABCD, with
4
AC 4 1 and AB 3 , BC
AD .
diagram not to scale
(a) Find BC .
(2)
(b) Show that
2 2
BD .
(2)
(c) Show that vectors BD and CA are perpendicular.
(3) (Total 7 marks)
7. Consider the points A(5, 8), B(3, 5) and C(8, 6).
(a) Find (i)
AB; (ii) AC .
(3)
(b) (i) Find AB AC .
(ii) Find the sine of the angle between
ABand AC .
(3) (Total 6 marks)
IB Questionbank Maths SL 3
8. A triangle has its vertices at A(–1, 3), B(3, 6) and C(–4, 4).
(a) Show that AB AC = –9.
(3)
(b) Find
BAˆC.
(4) (Total 7 marks)
9. A triangle has its vertices at A(–1, 3), B(3, 6) and C(–4, 4).
(a) Show that AB AC – 9
(b) Show that, to three significant figures, cos B A ˆ C – 0.569 .
(Total 6 marks)
10. The points A and B have the position vectors
2
2 and
1
3 respectively.
(a) (i) Find the vector
AB. (ii) Find AB .
(4)
The point D has position vector
23
d
(b) Find the vector
ADin terms of d.
(2)
The angle B A ˆ D is 90°.
(c) (i) Show that d = 7.
(ii) Write down the position vector of the point D.
(3) The quadrilateral ABCD is a rectangle.
(d) Find the position vector of the point C.
(4)
(e) Find the area of the rectangle ABCD.
(2) (Total 15 marks)
